<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<style type="text/css" style="display:none;"> P {margin-top:0;margin-bottom:0;} </style>
</head>
<body dir="ltr">
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
Hi Barry,</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
Thanks for your advice.</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
You are right on this. somehow there is some inconsistency when I compute the right hand side (true RHS + time-stepping contribution to the diagonal matrix) to compute the finite difference Jacobian. If I just use the call back function to recompute my RHS
before I call <b>MatMFFDSetBase</b>, then it works like a charm. But now I end up with computing my RHS three times. 1st time is to compute the true RHS, the rest two is for computing finite difference Jacobian.
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
In my previous buggy version, I only compute RHS twice. If possible, could you elaborate on your comments "<font face="Calibri, Helvetica, sans-serif">Also be careful about </font><span style="font-family:Calibri,Helvetica,sans-serif"> </span><span style="font-family:Calibri,Helvetica,sans-serif">petsc_baserhs</span>",
so I may possibly understand what was going on with my buggy version.</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
Besides, for a parallel implementation, my code already has its own partition method, is it possible to allow petsc read in a user-defined partition? if not what is a better way to do this?</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
Many thanks,</div>
<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
Feng<br>
</div>
<div>
<div id="appendonsend"></div>
<div style="font-family:Calibri,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0)">
<br>
</div>
<hr tabindex="-1" style="display:inline-block; width:98%">
<div id="divRplyFwdMsg" dir="ltr"><font style="font-size:11pt" face="Calibri, sans-serif" color="#000000"><b>From:</b> Barry Smith <bsmith@petsc.dev><br>
<b>Sent:</b> 11 March 2021 22:15<br>
<b>To:</b> feng wang <snailsoar@hotmail.com><br>
<b>Cc:</b> petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Subject:</b> Re: [petsc-users] Questions on matrix-free GMRES implementation</font>
<div> </div>
</div>
<div class="" style="word-wrap:break-word; line-break:after-white-space">
<div class=""><br class="">
</div>
Feng,
<div class=""><br class="">
</div>
<div class=""> The first thing to check is that for each linear solve that involves a new operator (values in the base vector) the MFFD matrix knows it is using a new operator. </div>
<div class=""><br class="">
</div>
<div class="">The easiest way is to call <font class="" face="Calibri, Helvetica, sans-serif">MatMFFDSetBase() before each solve that involves a new operator (new values in the base vector). Also be careful about </font><span class="" style="font-family:Calibri,Helvetica,sans-serif"> </span><span class="" style="font-family:Calibri,Helvetica,sans-serif">petsc_baserhs,
when you change the base vector's values you also need to change the </span><span class="" style="font-family:Calibri,Helvetica,sans-serif">petsc_baserhs values to the function evaluation at that point.</span></div>
<div class=""><span class="" style="font-family:Calibri,Helvetica,sans-serif"><br class="">
</span></div>
<div class=""><span class="" style="font-family:Calibri,Helvetica,sans-serif">If that is correct I would check with a trivial function evaluator to make sure the infrastructure is all set up correctly. For examples use for the matrix free a 1 4 1 operator applied
matrix free. </span></div>
<div class=""><br class="">
</div>
<div class="">Barry</div>
<div class=""><br class="">
</div>
<div class="">
<div><br class="">
<blockquote type="cite" class="">
<div class="">On Mar 11, 2021, at 7:35 AM, feng wang <<a href="mailto:snailsoar@hotmail.com" class="">snailsoar@hotmail.com</a>> wrote:</div>
<br class="x_Apple-interchange-newline">
<div class="">
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
Dear All,</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
<br class="">
</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
I am new to petsc and trying to implement a matrix-free GMRES. I have assembled an approximate Jacobian matrix just for preconditioning. After reading some previous questions on this topic, my approach is:</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
<br class="">
</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
the matrix-free matrix is created as:</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
<br class="">
</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
ierr = MatCreateMFFD(*A_COMM_WORLD, iqe*blocksize, iqe*blocksize, PETSC_DETERMINE, PETSC_DETERMINE, &petsc_A_mf); CHKERRQ(ierr);
<div class=""> ierr = MatMFFDSetFunction(petsc_A_mf, FormFunction_mf, this); CHKERRQ(ierr);</div>
<div class=""></div>
<div class=""><br class="">
</div>
<div class="">KSP linear operator is set up as:</div>
<div class=""><br class="">
</div>
<div class=""> ierr = KSPSetOperators(petsc_ksp, petsc_A_mf, petsc_A_pre); CHKERRQ(ierr); //petsc_A_pre is my assembled pre-conditioning matrix<br class="">
</div>
<div class=""><br class="">
</div>
<div class="">Before calling KSPSolve, I do:</div>
<div class=""><br class="">
</div>
ierr = MatMFFDSetBase(petsc_A_mf, petsc_csv, petsc_baserhs); CHKERRQ(ierr); //petsc_csv is the flow states, petsc_baserhs is the pre-computed right hand side</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
<br class="">
</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
The call back function is defined as:</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
<br class="">
</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
PetscErrorCode cFdDomain::FormFunction_mf(void *ctx, Vec in_vec, Vec out_vec)
<div class=""> {</div>
<div class=""> PetscErrorCode ierr;</div>
<div class=""> cFdDomain *user_ctx;</div>
<div class=""><br class="">
</div>
<div class=""> cout << "FormFunction_mf called\n";</div>
<div class=""><br class="">
</div>
<div class=""> //in_vec: flow states</div>
<div class=""> //out_vec: right hand side + diagonal contributions from CFL number</div>
<div class=""><br class="">
</div>
<div class=""> user_ctx = (cFdDomain*)ctx;</div>
<div class=""><br class="">
</div>
<div class=""> //get perturbed conservative variables from petsc</div>
<div class=""> user_ctx->petsc_getcsv(in_vec);</div>
<div class=""><br class="">
</div>
<div class=""> //get new right side</div>
<div class=""> user_ctx->petsc_fd_rhs();</div>
<div class=""><br class="">
</div>
<div class=""> //set new right hand side to the output vector</div>
<div class=""> user_ctx->petsc_setrhs(out_vec);</div>
<div class=""><br class="">
</div>
<div class=""> ierr = 0;</div>
<div class=""> return ierr;</div>
<div class=""> }</div>
</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
<br class="">
</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
The linear system I am solving is (J+D)x=RHS. J is the Jacobian matrix. D is a diagonal matrix and it is used to stabilise the solution at the start but reduced gradually when the solution moves on to recover Newton's method. I add D*x to the true right side
when non-linear function is computed to work out finite difference Jacobian, so when finite difference is used, it actually computes (J+D)*dx.<span class="x_Apple-converted-space"> </span><br class="">
</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
<br class="">
</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
The code runs but diverges in the end. If I don't do matrix-free and use my approximate Jacobian matrix, GMRES works. So something is wrong with my matrix-free implementation. Have I missed something in my implementation? Besides, is there a way to check
if the finite difference Jacobian matrix is computed correctly in a matrix-free implementation?</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
<br class="">
</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
Thanks for your help in advance.</div>
<div class="" style="font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; font-family:Calibri,Helvetica,sans-serif; font-size:12pt">
Feng <span class="x_Apple-converted-space"> </span></div>
</div>
</blockquote>
</div>
<br class="">
</div>
</div>
</div>
</body>
</html>